Spherical coordinate system
![Spherical coordinates (r, θ, φ) as commonly used in physics: radial distance r, polar angle θ (theta), and azimuthal angle φ (phi). The symbol ρ (rho) is often used instead of r.](/Images/godic/202412/21/3D_Spherical.svg1324.png")
![Spherical coordinates (r, θ, φ) as often used in mathematics: radial distance r, azimuthal angle θ, and polar angle φ. The meanings of θ and φ have been swapped compared to the physics convention.](/Images/godic/202412/21/3D_Spherical_2.svg1324.png")
![The output pattern of an industrial loudspeaker shown using spherical polar plots taken at six frequencies](/Images/godic/202412/21/Bosch_36W_column_loudspeaker_polar_pattern1324.png")
In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin, its polar angle measured from a fixed zenith direction, and the azimuth angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane.